Bonacich Eigenvector Power Centrality Calculator
Bonacich resolvent power α(I−βA)⁻¹A1over actual undirected binary network under caller contraction parameters. Not generic principal-eigenvector centrality or inferred influence; node order explicit and disconnected networks retained.
Description
Bonacich power combines a direct degree term with a weighted network-neighbor contribution.
Bonacich power combines a direct degree term with a weighted network-neighbor contribution.1
Its calibrated alpha and beta parameters define a fixed-point model rather than plain eigenvector centrality.
When to use Bonacich Eigenvector Power Centrality Calculator
Use this tool to obtain conditionalBonacichPowerByNode from the supplied records using the stated calculation. Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
How to use Bonacich Eigenvector Power Centrality Calculator and understand its results
- Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
- Enter observedAdjacency, callerAlpha, callerBeta, using the field meanings and rules below, then run the tool.
- Read result.conditionalBonacichPowerByNode. Use the units and sign conventions below, and review any unknown records separately.
- Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| observedAdjacency | Observed adjacency | numeric matrix | Required |
| callerAlpha | Caller alpha | number | Required |
| callerBeta | Caller beta | number | Required |
Require a symmetric binary zero-diagonal graph for two through 32 nodes, positive alpha and finite beta with abs(beta)×maximumDegree<0.9. Start with alpha times degree, then iterate alpha×degree+beta×adjacency×previousPower. Stop when maximum change is at most 1e−12 times max(1,largest absolute current value), or fail after 1024 iterations. Negative beta is accepted. Return this Bonacich fixed point, not normalized eigenvector centrality.
power=alpha×degree+beta×A×power Use the matching field units and the exact boundary, ordering and reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Calculated observation or qualified reference | object |
| result.conditionalBonacichPowerByNode | Converged alpha-degree plus beta-neighbor fixed-point values in node order. | list |
{
"input": {
"observedAdjacency": [
[
0,
1,
0
],
[
1,
0,
1
],
[
0,
1,
0
]
],
"callerAlpha": 1,
"callerBeta": 0
},
"output": {
"result": {
"conditionalBonacichPowerByNode": [
1,
2,
1
]
}
}
}Limitations and assumptions
Population definitions, survey design, calibration and observation coverage are independently established. A result describes the supplied record or conditional model without demonstrating causation, validating an instrument or supplying representative population evidence.
Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric matrices allow at most 128 rows and 128 columns, subject to the narrower shape requirements above. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related step, use Burt Network Constraint Efficiency Calculator: Ego network constraint measures direct and indirect dependence under an adopted tie normalization. For a complementary comparison, use Regular Equivalence Role Assigner Tool: Network role refinement groups nodes by the role types they reach and receive ties from.
References
Similar or alternative tools
- Burt Network Constraint Efficiency Calculator
Ego network constraint measures direct and indirect dependence under an adopted tie normalization.
- Regular Equivalence Role Assigner Tool
Network role refinement groups nodes by the role types they reach and receive ties from.